At the 7th of May, 2008, there was an article under www.wissenschaft.de teling that there may have been bodies of several dozen km diameter as trojans 390,000 km ahead and behind the Moon. From Earth they would have been as bright as Venus or Jupiter. The article refers to Jack Lissauer from NASA.

What about using that space for different pusposes like bystop towards the Moon, construction of a station and habitats, propellant depots and launchpoints into deep space?

What else do you imagine?

The points might be sufficient for buildings to be found in small towsn of around 50,000 inhabitants - although this is meant to illustrate the space only but not as a suggestion to colinize the points.

Your idea is entirely sensible, but like all reasonable ideas, it has already been around the block a few times. The idea of putting space colonies at the L5 libration point of the Earth-Moon system was suggested by Gerard O'Neill, which led to the formation of the L5 Society, now subsumed into the National Space Society. O'Neill further suggested using the L2 point as a place for a catcher, to intercept materials catapulted from the lunar surface by a mass-driver, for subsequent transport to L5.

Later work on orbital mechanics raised doubts about L5 being the most accessible place from both the Earth and the Moon. I don't know what the current thinking is.

Just this moment I thought of extending the point to the earthian Lagrange points of our orbit around the sun.

Probes might be sent there immediately without having to wait for a launch window on Earth. This could free launch pads and sites as well as orbits. The final launch wouldn't have to work against the earthian gravity and launch windows at those Lagrange points might be more favourable, better timed and so on.